Data Requirement for Species Tree from Multiple Gene Trees - - PowerPoint PPT Presentation

Data Requirement for Species Tree from Multiple Gene Trees

(Dasarathy, Nowak, Roch 2015)

Daewon Seo

• Mar. 14. 2017

Introduction

• Incomplete Lineage Sorting (ILS), ….
• Gene tree topologies could be different from species tree
• Two statistically consistent algorithms
• Key parameter : smallest species branch length
• Assuming perfect gene trees are given,

GLASS: # of genes ~ O

• STEAC: # of genes ~O

Introduction

• Focus on data length(≜ ), not number of genes(≜ )
• In a single gene tree, to reconstruct topology with high probability,

~O 1

• Therefore, in GLASS,

~O 1

• In STEAC,

~O 1

Introduction

• METAL
• Modified STEAC algorithm

~O

• for any 1  ~Θ
• While STEAC needs molecular clock assumption, METAL does not

Gene Tree Generation Process

• Given an unknown species tree,

: time of species tree

• : random time of gene tree branch

1

• Samples ~ JC model in each gene

tree

Gene1: ((A,B),C) Gene2: (A,(B,C)) - discordant

METAL

Concatenation is good!

METAL with molecular clock

• Take normalized Hamming distance of concatenated

sequence ̂ 1 ,

• [Thm 1] ̂ is ultrametric
• [Thm 2] UPGMA works! (other methods as well)
• To achieve error less than ,

and 1

METAL with non-molecular clock

• ̂ is no longer ultrametric, so a new metric satisfying

four-point condition is needed

if and only if

• Set

3 4 log 1 4 3 ̂

A B C D

METAL with non-molecular clock

• [Thm 3] satisfies the four-point condition
• Thus,
• log

1

• ̂ is our corrected distance
• [Thm 4] We can characterize the error probability of NJ over

,

• when is small enough

and 1

Discussion

• What is the exact tradeoff of , ?
• Hypothesis test argument gives ∈ Ω
• Steel and Szekely (2002), ∈ Ω

 ,

• This paper, ∈ , 1
• GLASS ∈ , ∈ ⇒ ∈
• What if mutation rate varies over gene trees?

Thank you!